I am using a mid 2017 iMac OS High Sierra. I have not upgrade beyond High Sierra because I depend upon IPhoto which will not run on newer OS's. I am about to buy a new iMac. What can replace iPhoto? I do not like the app iPhotos.

No matter what you change to there will be a learning curve. No two apps are the same. Photos is a natural progression from iPhoto, but if you don't like it then I think Mylio is closer to the "feel" of iPhoto, although more powerful than both. Lightroom CC is also more capable than Photos and but is a different feel from both.

After that you're into the serious hobbyist/professional applications like Lightroom Classic, On1 Photo Raw, CaptureOne and Exposure7

All of these apps require either a purchase or a subscription.

Unfortunately, you have missed one opportunity. Prior to Ventura, you could convert an iPhoto Library into a Photos Library, which kept some of the iPhoto structure.

In Ventura, and I assume going forward, you can only import your images from the iPhoto Library into a Photos one.

iPhoto '11, version 9.6.1 can also run on macOS 10.14 Mojave, but that is the end of the line.

Photos for Mac has changed a lot. The MOjave version is much better than the version you are seeing on High Sierra.

I am using Luminar Neo for editing my photos, as an editing extension from Photos.

But it is hard to suggest a replacement for iPhoto, you have to try them out, to see, which will best suit your workflow.